Combinatorics - NMUM208
Title: |
Kombinatorika |
Guaranteed by: |
Department of Mathematics Education (32-KDM) |
Faculty: |
Faculty of Mathematics and Physics |
Actual: |
from 2023 |
Semester: |
summer |
E-Credits: |
3 |
Hours per week, examination: |
summer s.:2/0, Ex [HT] |
Capacity: |
unlimited |
Min. number of students: |
unlimited |
4EU+: |
no |
Virtual mobility / capacity: |
no |
State of the course: |
cancelled |
Language: |
Czech |
Teaching methods: |
full-time |
Teaching methods: |
full-time |
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Guarantor: |
doc. RNDr. Antonín Slavík, Ph.D. |
Class: |
M Bc. MZV M Bc. MZV > Povinné M Bc. MZV > 2. ročník |
Classification: |
Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category |
Incompatibility : |
NMTM208, NMUM814, NUMP008 |
Interchangeability : |
NMTM208, NMUM814, NUMP008 |
Is incompatible with: |
NUMP008, NMUM814, NMTM208 |
Is interchangeable with: |
NMUM814, NMTM208, NUMP008 |
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Annotation -
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Last update: T_KDM (24.04.2017)
An introductory course in classical combinatorics.
Last update: T_KDM (24.04.2017)
Úvodní přednáška z kombinatoriky zejména pro studenty učitelství.
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Course completion requirements - Czech | |
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Last update: doc. RNDr. Antonín Slavík, Ph.D. (07.06.2019)
Písemná zkouška |
Literature -
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Last update: T_KDM (29.04.2013)
- R. B. J. T. Allenby, A. Slomson: How To Count. An Introduction to Combinatorics, CRC Press, 2011.
- J. M. Harris, J. L. Hirst, M. J. Mossinghoff: Combinatorics and Graph Theory, Springer, 2008.
- J. Matoušek, J. Nešetřil: Invitation to Discrete Mathematics, Oxford University Press, 2008.
- N. Ya. Vilenkin: Combinatorics, Academic Press, 1971.
- R. L. Graham, D. E. Knuth, O. Patashnik: Concrete Mathematics, Addison-Wesley, 1994.
Last update: T_KDM (29.04.2013)
- R. B. J. T. Allenby, A. Slomson: How To Count. An Introduction to Combinatorics, CRC Press, 2011.
- J. M. Harris, J. L. Hirst, M. J. Mossinghoff: Combinatorics and Graph Theory, Springer, 2008.
- E. Calda: Kombinatorika pro učitelské studium, Matfyzpress, 1996.
- J. Matoušek, J. Nešetřil: Kapitoly z diskrétní matematiky, Karolinum, 2000.
- N. J. Vilenkin: Kombinatorika, SNTL Praha, 1960.
- R. L. Graham, D. E. Knuth, O. Patashnik: Concrete Mathematics, Addison-Wesley, 1994.
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Requirements to the exam - Czech | |
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Last update: doc. RNDr. Antonín Slavík, Ph.D. (07.06.2019)
Zkouška sestává ze čtyř příkladů z témat, která korespondují s obsahem přednášky. |
Syllabus -
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Last update: T_KDM (24.04.2017)
- High school combinatorics.
- Inclusion-exclusion principle, derangements.
- Rook polynomials and permutations with forbidden positions.
- The twelvefold way (distributing objects into boxes).
- Recurrent problems and their solution, Fibonacci numbers and their properties.
- Generating functions and their use in solving recurrences.
- Combinatorial applications of polynomials and infinite series.
- Combinatorial identities.
Last update: T_KDM (24.04.2017)
- Kombinatorika na střední škole (kombinatorické pravidlo součtu a součinu, variace, permutace, kombinace).
- Princip inkluze a exkluze, permutace bez pevných bodů.
- Věžové polynomy a permutace s omezujícími podmínkami.
- Úlohy vedoucí na rekurentní rovnice a jejich řešení, Fibonacciova čísla a jejich vlastnosti.
- Generující funkce, jejich použití k řešení rekurentních rovnic.
- Kombinatorické aplikace polynomů a řad.
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